1. **State the problem:** Solve the equation $$-0.8(10 - x) = 36$$ for $x$. 2. **Use the distributive property:** Multiply $-0.8$ by each term inside the parentheses. $$-0.8 \times 10 + (-0.8) \times (-x) = 36$$ 3. **Simplify:** $$-8 + 0.8x = 36$$ 4. **Isolate the variable term:** Add 8 to both sides. $$-8 + 0.8x + 8 = 36 + 8$$ $$0.8x = 44$$ 5. **Solve for $x$:** Divide both sides by 0.8. $$x = \frac{44}{0.8}$$ Show cancellation: $$x = \frac{\cancel{44}}{\cancel{0.8}} \times \frac{10}{10} = \frac{440}{8}$$ 6. **Simplify the fraction:** $$x = 55$$ **Final answer:** $$x = 55$$